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Mathematical models of decision processes for dispersing animals Public Deposited

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  • Each chapter in this expository paper considers a mathematical model of an aspect of animal behavior, and how it affects the patterns of movement across and within a landscape. These models are all directly or indirectly related to questions in either Behavioral Ecology or Landscape Ecology, or both. I first learned about Ecologists’ efforts to connect Landscape Ecology with Behavioral Ecology when Dr. Judy Stamps, Emerita of the University of California, Davis, visited the IGERT colloquium at OSU in the Fall of 2008. Landscape Ecology focuses on neighborhoods, groups, and populations of animals and plants, which are all linked together by the process of dispersal. By contrast, Behavioral Ecology focuses on decisions made by individual dispersers – how they forage for food, select mates, and settle in habitat. Stamps ([27], [18], [26]) argues that this last process – the process of habitat selection –was one way to bridge the gap between Landscape Ecology and Behavioral Ecology. To this end, we introduce and develop three individual-based models of dispersal. Most of our efforts have gone into Chapter 1, where we develop a Stochastic Dynamic Pro-gramming model of habitat selection in natally-dispersing brush mice. The individual choices that brush mice make to investigate, return to, and eventually settle in different habitat sites across the landscape are shown to affect their overall patterns of dispersal: the average time spent on this process, the quality of the site achieved by the process, and the length of the refractory period –the time during which an individual will not settle in response to cues from a habitat. In Chapter 2, we consider a challenge offered by Brillinger [3], regarding the simulation of animal movement constrained to a bounded landscape. As an example model of constrained animal motion, we consider a diffusion model constrained to an interval and study its properties and the conditions on them, for example the conditions for ergodicity and the existence of a stationary distribution. Determining these conditions is an important first step if one wants to make any statistical comparison to data from animal movement. Seeley, Visscher, & Passino [22] document a fascinating example of democratic animal behavior. This example is in the swarming behavior of honeybees selecting a new site for a colony which has split off from its home. The process by which they make their decision is highly democratic, and Seeley himself has started employing a version of it in departmental meetings. In Chapter 3, we consider a model to study the efficacy of swarms using a range of methods to distribute and deploy their scouts for search, and with different memory capacities. We are aware of one other simulation model of this behavior [15], which we introduce for the purposes of comparing and contrasting with our own. We present preliminary results, but note that this chapter is included more as a reference point for future work rather than for the presented, preliminary results.
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